central limit theorem

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cen·tral lim·it the·o·rem

the sum (or average) of n realizations of the same process, provided only that it has a finite variance, will approach the gaussian distribution as n becomes indefinitely large. This theory provides a broad warrant for the use of normal theory even for nongaussian data. In the form stated here, it constitutes the classical version; more general versions allow serious relaxation of the usual assumptions.
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Alternatively, by the asymptotic normality of the MLE, the approximate 100(1 - [alpha])% CIs for [mu] and [sigma] can be obtained as
Heinrich and Prokesova (2010) proved that if P is a stationary point process, with milder mixing conditions than the ones required for the asymptotic normality of the corresponding counting measure, and if [{[W.
Consistency and uniformly asymptotic normality of wavelet estimator in regression model with assoeiated samples, Statist.
1) states the asymptotic normality of [square root of T] [bar.
Before stating our result, we mention that the asymptotic normality of [X.
where, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is a quadratic form obtained as a consequence of the asymptotic normality described in (3).
In any case one can invoke the Central Limit Theorem for asymptotic normality because the sample size is large.
Mahmoud, Smythe and Szymanski (12) used a representation with a generalized Polya urn to prove the asymptotic normality (1.
1973, On the Asymptotic Normality of the Maximum-Likelihood Estimate When Sampling From a Stable Distribution, Annals of Statistics, 1: 948-957.
GMTs of antibody and their confidence intervals were computed by transforming the results to a logarithmic scale, assuming asymptotic normality conditions were satisfied on the scale and converting back to the original scale.
1996) Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH (1,1).
The consistency and asymptotic normality of the QMLE has been established only for specific special cases of the ARFIMA and/or FIGARCH model.
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